Barber, a former aide to Giffords, won her seat in a special election in June following a shooting the year before in Tucson at a “Congress On Your Corner” event. Giffords, then in her third term as a congresswoman, was shot in the head. She later left Congress to focus on her recovery and endorsed Barber as her successor.

Barber also was wounded in the leg and cheek during the shooting; six others were killed.

As of Saturday, Barber led McSally by 1,402-vote margin with more than 285,000 ballots cast.

Democrats maintain a slight lead in each of the two additional House races that remain too close to call. A third unresolved House race in Louisiana will pit two Republican incumbents against each other in a December 8 run-off election.

The balance of power now stands at 234 Republicans, which includes the winner of the Louisiana race, and 199 Democrats. Before the election, Republicans held 242 seats and Democrats had 193.

The remaining races are Florida’s 18th district between Republican incumbent Rep. Allen West and Democrat Patrick Murphy and North Carolina’s 7th district between Republican David Rouzer and Democratic incumbent Rep. Mike McIntyre.

CNN’s Dana Davidsen, Kevin Bohn and Robert Yoon contributed to this report.